A pearl of mass m is in a position to slide over a smooth wire. At the initial instant the pearl is in the middle of the wire. The wire moves linearly in a horizontal plane with an acceleration a in a direction having angle θ θ with the wire. The acceleration of the pearl with reference to wire is
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Let a x , a y and a r be the net leftward horizontal acceleration bead, net downward vertical acceleration of bead and relative acceleration of bead with reference to rod respectively. Then
a y = a r cos θ θ + a
and a x = a r sin θ θ
Projecting forces vertically and horizontally
mg – N cos θ θ = ma r + ma cos θ θ
i.e., a r = g sin θ θ - a cos θ θ
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